Yevamos 1:3 - 1:4

שש עריות חמורות מאלו – and what is their stringency? That they are married to others (i.e., outsiders). But they are not able to marry the brother of this one from his father, and if their husbands died, who are “strangers” (i.e., outsiders) regarding this one, their rival/co-wives are permitted to marry to this one, for the rivals of a woman are not forbidden on account of consanguinity other than when she falls before him for levirate marriage from his brother. And our Rabbi/teacher, Moshe bar Maimon (i.e., Maimonides) explained, that if they married through sin to his brother and he died without children, and they fell [before him] for levirate marriage, their rival/co-wives are permitted, for these are not [forbidden] on account of consanguinity since their betrothal/Kiddushin do not take effect to his brother in those forbidden relations of incest.

אמו – she cannot marry his brother from his father, for she is to him the wife of the father, according to the one who says that the ravaged wife of his father is prohibited, and above (Mishnah two), I explained, that this is not the Halakha, but rather, his mother exempts her rival/co-wife, for she is able to marry to his brother from his father.

אשת אביו אשת אחיו מאביו – [that he had children] and the sister of his father, all of them are forbidden to his brother, like they are forbidden to him, and there is not side of Levirate marriage on this forever, and if others married them and they have other wives, and they (i.e., the husbands) died, their rival/co-wives are permitted to marry this one, and similarly, if his brother married them in sin, and he died without children, their rival/co-wives are permitted.

בית שמאי מתירין – the rival of a woman forbidden on account of consanguinity is to be married by the levir, for they (i.e., the School of Shammai) lack this exposition/Midrashic interpretation of (Leviticus 18:18): “[Do not marry a woman] as a rival [to her sister and uncover her nakedness in the other’s lifetime].”

חלצו – [they performed the ritual of Halitzah] the rival/co-wives from the brothers.

בית שמאי פוסלין – the rival/co-wives from the priesthood, since their [act of] Halitzah is [considered] Halitzah.

ובית הלל מכשירין – that their [act of] Halitzah was not a necessity and she is considered as one who performed Halitzah from a heathen/foreigner.

נתיבמו – to brothers.

בית שמאי מכשירין – [The School of Shammai validates them] to Kohanim, if they had become widowed from their levirs.

ובית הלל פוסלים – that they had engaged in sexual relationship with those forbidden to them, and one who engages in sexual relations with one prohibited to her makes her a harlot, and a harlot is prohibited to [marry] a Kohen.

לא נמנעו – and even though that the children of the rival/co-wives who had been married by the levir that according to the School of Shammai are Mamzerim/illegitimate according to the School of Hillel, and they are [included] in the prohibition of marrying the wife of one’s brother upon them, and the [violation of] the [marriage of the] wife of one’s brother is [liable to] extirpation, and those who are liable for extirpation are considered Mamzerim/illegitimate, nevertheless, [members of] the School of Hillel were not prevented from marrying women from the School of Shammai, because they would inform them of those women coming from the rival/co-wives and separate from them.

אלו על גבי אלו – they would loan their utensils one to the other. And in the Gemara (Tractate Yevamot 14a), raises an objection on that which is taught [in our Mishnah]: “The School of Shammai declares that the rival/co-wives are permitted [to enter into levirate marriage with] the brothers and the School of Hillel [prohibits] . They call it here (Deuteronomy 14:1): “You shall not gash yourselves/לא תתגדדו “ – do not form yourselves into religious [factions]. And they responded – such as the case of one Jewish court in one city – where half teach according to the School of Shammai and half teach according to the School of Hillel, but [where there are] two Jewish courts in one city, and all the more so, two Jewish courts in two towns, it does not matter.