αὗταιtheseNominativedemonstrative pronoun (subject of the summarizing clause)οὗτος, αὕτη, τοῦτο: the feminine plural αὗται ('these [cities]') opens the recapitulating summary, gathering the six named cities under one heading.
αἱtheNominativearticle (with πόλεις)αἱ: Greek article marking definiteness and the role of the accompanying noun phrase.
πόλειςcitiesNominativepredicate/subject noun (with αὗται: 'these cities')πόλις (pl. πόλεις): 'city'; the head-noun of the summary, referring back to the six refuge-cities just enumerated.
αἱtheNominativearticle (attributive, with ἐπίκλητοι)αἱ: Greek article marking definiteness and the role of the accompanying noun phrase.
ἐπίκλητοιappointed / designatedNominativeattributive adjective (with second article: 'the appointed cities')ἐπίκλητος: 'called-out / summoned / designated'; a verbal adjective from ἐπικαλέω; renders מוּעָדָה / the notion of cities formally 'designated' for asylum; the second-article construction (αἱ πόλεις αἱ ἐπίκλητοι) makes it emphatically attributive.
τοῖςthe / forDativearticle (with υἱοῖς)τοῖς: Greek article marking definiteness and the role of the accompanying noun phrase.
υἱοῖςsonsDativedative of advantage ('for the sons of Israel')υἱός (pl. dat. υἱοῖς): the dative of advantage marks the native Israelites as the primary beneficiaries of the asylum-cities.
ΙσραηλIsraelgenitive of relationship (indeclinable: 'sons of Israel')Ισραηλ: indeclinable; genitive of relationship with υἱοῖς.
καὶandcoordinate conjunction (extending the provision to the alien)καὶ: connective element linking clauses, phrases, or discourse developments in the passage.
τῷthe / forDativearticle (with προσηλύτῳ)τῷ: Greek article marking definiteness and the role of the accompanying noun phrase.
προσηλύτῳsojourner / proselyteDativedative of advantage ('for the resident alien')προσήλυτος: 'newcomer / resident alien / sojourner'; the LXX coinage rendering גֵּר; in pre-rabbinic usage it denotes the foreigner dwelling among Israel rather than the later technical 'convert'; its inclusion enacts the one-law principle (Num 35:15).
τῷthe / whoDativearticle (substantivizing the participle προσκειμένῳ)τῷ: Greek article marking definiteness and the role of the accompanying noun phrase.
προσκειμένῳwho attaches himself / dwellsPres Mid Part Dat Masc Sg · πρόσκειμαιattributive participle (modifying προσηλύτῳ: 'who attaches himself')→ customary present participle (the alien's ongoing residence)πρόσκειμαι: 'lie near / be attached to / adhere'; the present participle τῷ προσκειμένῳ ἐν αὐτοῖς describes the alien who has joined himself to / settled among the Israelites; renders the Hebrew גֵּר construction for the sojourner who has thrown in his lot with Israel.
ἐνin / amongpreposition + dative (locative: 'among them')ἐν: preposition governing its complement and marking the relation specified by the clause.
αὐτοῖςthemDativedative object of ἐν (the Israelites among whom the alien dwells)αὐτός (dat. pl. αὐτοῖς): the personal pronoun refers to the sons of Israel; ἐν αὐτοῖς ('among them') locates the sojourner within the community he has joined.
καταφυγεῖνto flee for refugeAor Act Inf · καταφεύγωepexegetic infinitive (defining the purpose of the appointed cities)→ ingressive aorist infinitive (the act of fleeing to refuge)καταφεύγω: 'flee for refuge / take asylum'; the compound κατα- intensifies φεύγω toward a place of safety; the infinitive καταφυγεῖν explains the cities' designated function — they exist precisely so that the killer may flee there.
ἐκεῖthereadverb of place (goal of the fleeing)ἐκεῖ: 'there / to that place'; renders שָׁמָּה; points to the refuge-cities as the destination of the manslayer's flight.
παντὶfor everyoneDativedative of advantage (distributive: 'for everyone who strikes')πᾶς (dat. παντί): 'all / every / everyone'; the distributive dative universalizes the provision — it applies to any and every unintentional killer, Israelite or alien.
παίοντιwho strikesPres Act Part Dat Masc Sg · παίωattributive participle (modifying παντί: 'everyone striking')→ general/customary present participle (any case of fatal striking)παίω: 'strike / smite / hit'; the present participle here functions generically ('anyone who strikes'); a near-synonym of πατάσσω in v. 3, varying the verb while restating the same condition of unintentional homicide.
ψυχὴνa person / lifeAccusativedirect object of παίοντιψυχή: 'soul / life / person'; the object of the fatal blow, as in v. 3.
ἀκουσίωςunintentionallyadverb of manner (qualifying παίοντι)ἀκουσίως: 'unintentionally / by accident'; renders בִּשְׁגָגָה; repeats the decisive legal qualifier of v. 3, confining the asylum to inadvertent killing.
ἵναso thatpurpose conjunction (with subjunctive ἀποθάνῃ)ἵνα: 'in order that / so that'; introduces the purpose clause expressing the protective aim of the refuge — that the killer not be slain.
μὴnotnegative particle (negating the subjunctive in the purpose clause)μή: the subjective negative used with the subjunctive in purpose clauses ('so that he may not die').
ἀποθάνῃhe may dieAor Act Subj 3 Sg · ἀποθνῄσκωverb of negative purpose clause (subjunctive with ἵνα μή)→ ingressive aorist subjunctive (the feared event of being killed)ἀποθνῄσκω (aor. subj. ἀποθάνῃ): 'die'; the subjunctive in the negated purpose clause names the outcome the refuge is meant to prevent — summary death at the avenger's hand.
ἐνin / bypreposition + dative (instrumental: 'by the hand of')ἐν + dative: here instrumental, in the Hebraizing idiom ἐν χειρί ('by the hand of') = 'at the hands of'.
χειρὶhandDativedative of means (idiomatic: 'by the hand of')χείρ (dat. χειρί): 'hand'; the idiom ἐν χειρί renders בְּיַד ('by the hand of / through the agency of'); a Hebraism for personal agency, here that of the blood-avenger.
τοῦthe / of theGenitivearticle (substantivizing the participle ἀγχιστεύοντος)τοῦ: Greek article marking definiteness and the role of the accompanying noun phrase.
ἀγχιστεύοντοςone who avengesPres Act Part Gen Masc Sg · ἀγχιστεύωsubstantival participle (genitive: 'of the one avenging the blood')→ customary present participle (the standing role of the blood-avenger)ἀγχιστεύω: 'act as kinsman-redeemer / avenger'; ὁ ἀγχιστεύων τὸ αἷμα renders גֹּאֵל הַדָּם; the same phrase as in v. 3, forming a verbal inclusio around the chapter's asylum-law.
τὸtheAccusativearticle (with αἷμα)τὸ: Greek article marking definiteness and the role of the accompanying noun phrase.
αἷμαbloodAccusativedirect object of ἀγχιστεύοντος ('avenging the blood')αἷμα: 'blood'; renders דָּם; the shed blood the kinsman is bound to requite; the accusative object of ἀγχιστεύω, as in v. 3.
ἕωςuntiltemporal conjunction (with ἂν + subjunctive)ἕως: 'until'; marks the temporal limit of the protection, as in v. 3.
ἂν(modal particle)modal particle (with ἕως and subjunctive: indefinite future time)ἄν: the modal particle lending contingency to the ἕως-clause ('until such time as').
καταστῇhe stands / is presentedAor Act Subj 3 Sg · καθίστημιverb of temporal clause (subjunctive with ἕως ἂν)→ ingressive aorist subjunctive (presenting oneself for trial)καθίστημι (aor. subj. καταστῇ): 'present oneself / stand (for judgment)'; repeats the verb of v. 3, again marking submission to the congregation's adjudication as the terminus of the asylum.
ἔναντιbefore / in the presence ofpreposition + genitive (location of the trial)ἔναντι: 'before / in the presence of'; a near-equivalent of ἐναντίον used in v. 3; both render לִפְנֵי; the slight lexical variation is characteristic of the LXX's flexible rendering of the Hebrew preposition.
τῆςthe / of theGenitivearticle (with συναγωγῆς)τῆς: Greek article marking definiteness and the role of the accompanying noun phrase.
συναγωγῆςcongregationGenitivegenitive object of ἔναντισυναγωγή: 'assembly / congregation'; renders עֵדָה; the adjudicating community of Israel, as in v. 3, closing the inclusio.
εἰςfor / untopreposition + accusative (purpose / goal)εἰς: preposition governing its complement and marking the relation specified by the clause.
κρίσινjudgmentAccusativeaccusative object of εἰς (purpose: 'for judgment')κρίσις: 'judgment / trial'; renders מִשְׁפָּט; the chapter's final word, sealing the asylum-law with the requirement of due legal process — the manslayer's fate rests on judicial determination, not on private vengeance.