15 Though thou, Israel, play the harlot, yet let not Judah offend; and come not ye unto Gilgal, neither go ye up to Beth-aven, nor swear, The LORD liveth.
[AD 420] Jerome on Hosea 4:15-16
"If you fornicate, Israel, let not at least Judah sin, and do not enter into Gilgal, and do not ascend into Bethaven, neither shall you swear, by the living Lord, for as an wanton heifer, Israel has sinned. Now the Lord will feed them as a lamb in a large place." LXX: "But you, Israel, do not ignore, and Judah, do not enter into Galgala, nor ascend into the house [ὢν] and do not swear, the Lord lives: for as a refuge-killed cow, Israel went insane. Now the Lord will feed them like a lamb in a spacious place." "For home" [ὢν] being read in some copies, and most particularly in Theodotion as "house of iniquity," which Aquila and Symmachus interpreted as ἀνωφελοῦς ["house of the profitless,"] that is, "useless" which is of no benefit, and is designated by another word "idol". But Bethel was formerly called the "House of God," but after the calves were placed in it, it was called "Bethaven," that is, "useless house" and "house of idols," which we have expressed as we read it in Hebrew. But it seems to me that both the people of Israel and Jeroboam the son of Nebat made a golden calf to be worshipped in the wilderness, and fashioned golden calves as they had learned in Egypt, where the bulls are worshipped as gods in their superstition. Let us discuss the meaning of the chapter: Sisemel, O Israel, you have been deceived by error and have mixed with prostitutes, so that whoever fulfills the act of offering and giving gifts to the king or himself, would become a priest of the high places. At least you, Judah, who possess Jerusalem and have Levites from the law and perform temple ceremonies, should not imitate the examples of your former sister Oolla in fornication and worship idols with her. Do not enter Galgala, about which we read in this same prophet: 'All their wickedness is in Galgala' (Hosea 9:15), where Saul was anointed king, where the people, coming out of the wilderness, camped for the first time, and were purified by a second circumcision. From that time on, in this notorious place, error of an opposing religion crept in. And do not go up to Bethaven, that is, what was once called Bethel, because after golden calves were placed there by Jeroboam son of Nabath, it is not called the House of God but the house of an idol. For which reason, I wonder why the Septuagint interpreted it as "unless I make a mistake, the middle Jod letter which is surrounded on both sides by Aleph and Nun letters was believed to be Vau based solely on its size." "You shall not make a false oath by my name," says the Lord. For I do not want my name to be mentioned on your lips, which is tainted by the memory of idols. For just as a cow that is wanton and throws off her yoke, so too Israel, that is, the ten tribes, turned away from the service of the Lord. For the wanton cow, the Seventy translated παροιστρῶσαν, which stung by desire and struck by the asylum, which they commonly call "tabanus". About which Virgil also reports in the third book of the Georgics.

...The name of the asylum is Roman: the Greeks called it "oestrum," a harsh and bitter name that drives all the herds to flee in terror from the woods. The sky roars and trembles with their cries, and the banks of the dry Tanagra shake. And so because Israel had become insane and, struck by the spirit of fornication, went mad with unbelievable fury, not much longer afterwards, but while the prophet's body was still possessed by the spirit, the Lord said: "I will feed them as a lamb in a spacious place." He kept the metaphor of a cow in heat, in the same way that he had used it before, calling the captivity in Assyria and the dispersion of Israel into the widest land of the Medes, the pasture of a wide field and of flocks of sheep and lambs. A predisposition is present against heretics, concerning whom or about whom it is said: If you fornicate once, heretic, at least, do not offend, church-goer, and do not enter into Galgala, the meetings of heretics, where the sins of everyone are exposed, and are rolled in the mud like pigs. Do not assume that you rise up to the proud and arrogant fictions of false teachings. For there is not the house of God, but the house of an idol. And do not swear by the name of Christ, whose majesty you have defiled by mingling it with idols. For just as a slaughtered cow falls in the asylum, so the heretics are struck by the burning arrows of the devil and abandon knowledge of the Law. Therefore, they will graze in the broad and spacious way that leads to death, and the patience of the Lord and the care of the good Shepherd will nourish them unto their own destruction.

[AD 1781] Richard Challoner on Hosea 4:15
Not into Galgal, and come not up into Bethaven: Places where idols were worshipped. Bethel, which signifies the house of God, is called by the prophet, Bethaven, that is, the house of vanity, from Jeroboam's golden calf that was worshipped there.