4.8

परित्राणाय साधूनां विनाशाय च दुष्कृताम् ।
धर्मसंस्थापनार्थाय सम्भवामि युगे युगे ॥

paritrāṇāya sādhūnāṃ vināśāya ca duṣkṛtām
dharmasaṃsthāpanārthāya sambhavāmi yuge yuge

Kṛṣṇa (कृष्ण) is still speaking, to Arjuna.

The verse

For the protection of the good, for the ruin of those who do harm, and to make dharma stand, I come to be age after age.

नेपालीमा

सज्जनको रक्षाका लागि, हानि गर्नेहरूको नाशका लागि, र धर्मलाई खडा गर्न म युग युगमा उत्पन्न हुन्छु।

Where it sits

4.7 gave the occasion, and this verse gives the three ends, tying the coming-forth to every age, not to Kurukṣetra (कुरुक्षेत्र) alone. The birth Arjuna asked about is one of these.

Split: परित्राणाय + साधूनाम् + विनाशाय + च + दुष्कृताम् + धर्म-संस्थापन-अर्थाय + सम्भवामि + युगे + युगे

paritrāṇāya + sādhūnām + vināśāya + ca + duṣkṛtām + dharma-saṃsthāpana-arthāya + sambhavāmi + yuge + yuge

Sanskrit, in depth

The words

देवनागरीWordGrammarSense
परित्राणायparitrāṇāyadative singularfor protection.
साधूनाम्sādhūnāmgenitive pluralof the good. The people who hold to what is right.
विनाशायvināśāyadative singularfor ruin, for destruction.
चcaindeclinableand.
दुष्कृताम्duṣkṛtāmgenitive pluralof those who do harm. duṣ (दुष्) "badly," kṛt (कृत्) "a doer."
धर्म-संस्थापन-अर्थायdharma-saṃsthāpana-arthāyadative singularfor the sake of making dharma stand. saṃsthāpana (संस्थापन) is the setting-up. artha (अर्थ) at the end of a dative compound is "for the sake of."
सम्भवामिsambhavāmipresent, 1st singularI come to be.
युगेyugelocative singularin an age.
युगेyugelocative singularin an age. Said twice: age after age.

The phrases

paritrāṇāya sādhūnām (परित्राणाय साधूनाम्) is the first purpose. For the protection of the good. The dative is the "for," and the genitive is whose protection.

vināśāya ca duṣkṛtām (विनाशाय च दुष्कृताम्) is the second. And for the ruin of those who do harm. Same pair of cases.

dharmasaṃsthāpanārthāya sambhavāmi yuge yuge (धर्मसंस्थापनार्थाय सम्भवामि युगे युगे) is the third purpose, and the verb. I come to be, age after age, for the sake of making dharma stand. The two locatives are not two different ages named. The repetition is the rhythm of 4.7's doubled yadā (यदा).

Sanskrit in this line

Three datives of purpose answer "what for": paritrāṇāya (परित्राणाय), vināśāya (विनाशाय), and arthāya (अर्थाय) at the end of the long compound. A dative of purpose does not need a preposition. The ending --āya (आय) is the "for." Each one hangs on sambhavāmi (सम्भवामि).

Say it back

Three purposes, then the verb. If yuge (युगे) is said once, the coming-forth has been made a single event. Stay here.