saha-yajñāḥ prajāḥ sṛṣṭvā
purovāca prajāpatiḥ
anena prasaviṣyadhvam
eṣa vo ‘stv iṣṭa-kāma-dhuk

Translation of Bhagavad Gita 3.10

In the beginning of creation, the Lord of all creatures sent forth generations of men and demigods, along with sacrifices for Vishnu, and blessed them by saying, “Be thou happy by this yajna [sacrifice] because its performance will bestow upon you everything desirable for living happily and achieving liberation.”

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

The material creation by the Lord of creatures (Vishnu) is a chance offered to the conditioned souls to come back home—back to Godhead. All living entities within the material creation are conditioned by material nature because of their forgetfulness of their relationship to Vishnu, or Krishna, the Supreme Personality of Godhead. The Vedic principles are to help us understand this eternal relation, as it is stated in the Bhagavad-gita: vedais ca sarvair aham eva vedyah. The Lord says that the purpose of the Vedas is to understand Him. In the Vedic hymns it is said: patim vishvasyatmesvaram. Therefore, the Lord of the living entities is the Supreme Personality of Godhead, Vishnu. In the Srimad-Bhagavatam also (2.4.20) Srila Shukadeva Gosvami describes the Lord as pati in so many ways:

sriyah patir yajna-patih praja-patir
dhiyam patir loka-patir dhara-patih
patir gatis candhaka-vrsni-satvatam
prasidatam me bhagavan satam patih

The praja-pati is Lord Vishnu, and He is the Lord of all living creatures, all worlds, and all beauties, and the protector of everyone. The Lord created this material world to enable the conditioned souls to learn how to perform yajnas (sacrifices) for the satisfaction of Vishnu, so that while in the material world they can live very comfortably without anxiety and after finishing the present material body they can enter into the kingdom of God. That is the whole program for the conditioned soul. By performance of yajna, the conditioned souls gradually become Krishna conscious and become godly in all respects. In the Age of Kali, the sankirtana-yajna (the chanting of the names of God) is recommended by the Vedic scriptures, and this transcendental system was introduced by Lord Caitanya for the deliverance of all men in this age. Sankirtana-yajna and Krishna consciousness go well together. Lord Krishna in His devotional form (as Lord Caitanya) is mentioned in the Srimad-Bhagavatam (11.5.32) as follows, with special reference to the sankirtana-yajna:

krishna-varnam tvisakrishnam
yajnaih sankirtana-prayair
yajanti hi su-medhasah

“In this Age of Kali, people who are endowed with sufficient intelligence will worship the Lord, who is accompanied by His associates, by performance of sankirtana-yajna.” Other yajnas prescribed in the Vedic literatures are not easy to perform in this Age of Kali, but the sankirtana-yajna is easy and sublime for all purposes, as recommended in Bhagavad-gita also (9.14).

Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

Therefore, one with impure heart should perform actions without desire, rather than give up action. Now, if you cannot be desireless in the actions, then you should still perform actions offered to Visnu  with  desire, rather   than  give  up  actions completely. This is explained in seven verses.

Long ago,  along with yajna, Brahma  created  the  creature qualified for offering to Visnu and said, “Increase more and more the population by this dharma or yajna. May this yajna bestow all desired enjoyment (ista kama dhuk).” By this he indicated that they had material desires.

The compound saha-yajna is formed by the rule vopasarjanasya (Panini 6.3.82). The compound saha-yajna is used instead of sa-yajna.

Commentary by Sri Ramanuja of Sri Sampradaya:

3.10 As there is the scriptural text beginning with ‘The Lord of Universe’ (Tai. Na., 11.3), it is justifiable to take the term Prajapati in its wider connotation and interpret it to mean Narayana who is the Lord of all beings, the creator of the universe and the Self of the universe. In the beginning, i.e., during the creation, He, the Lord of beings, saw all beings helpless by their conjunction with beginningless non-conscient matter, bereft of the distinctions of name and form, and submerged in Himself. They were incapable of attaining the major ends of human existence, being almost one with non-conscient matter. He, the supremely compassionate, with a desire to resuscitate them, created them together with sacrifice in order that they might perform sacrifices as His worship and said: ‘By this sacrifice, shall you prosper,’ i.e., multiply and prosper. May this sacrifice fulfil your supreme object of desire called release (Moksa) and also the other desires that are in conformity with it. How, then, should this be done?

Commentary by Sri Sridhara Swami of Rudra Sampradaya:

So we see that not only Lord Krishna is stating this but also according to Prajapati or Brahma the creator of all material beings, that one who performs actions is superior to one who performs no actions. This is being explained in this and the next three verses. The words saha-yagnah-prajah means all progeny in existence in general but specifically the brahmans and ksatriyas who perform worship according to the Vedic scriptures. Verily remembering Lord Krishna and chanting His holy names is yagna or worship and by such sacrifice mankind will flourish and prosper. Here the word yagna means the time sacrificed to do the daily duties offered to the Supreme Lord and other obligatory activities such as following Ekadasi. Although there is no question of praising work that is done with desires it still exhibits that in general actions are better than inertness and lassitude which are more objectionable.

Commentary by Sri Madhvacharya of Brahma Sampradaya:

Sri Madhvacharya did not comment on this sloka.

Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

Here Lord Krishna reveals the words of Prajapati or Brahma the creator of the forms and categories of material beings and the arranger of the material manifestation. Here it states that one desiring liberation should perform selfless actions with the thought of appeasement and propitiation to the Supreme Lord. Now Lord Krishna is infering that he teaches this knowledge of propitiatiopn to His devotees only. This is because Brahma has given facilty for beings other than the devotees to worship in appeasement lesser gods such as the demi-gods. Thus after Brahma created mankind he instructed the three twice born classes of brahmins, ksatriyas and vaisyas to perform selfless actions in the spirit of worship of the Supreme Lord and this will be for you sacrifice. Sacrifing the desires for reward and attachment to the results and in this way mankind will flourish and prosper. The actual understanding is that this spirit of sacrifice perfromed with faith acording to ones status and stage in life will bequeath all auspiciousness in this life and the next life. Such instructions for such wishfulfilling actions and the confusion that might arise to due to them from statements of non- attachment earlier in this chapter in verses four, seven and seventeen as well as refering to delighting in the atma or soul in this chapter in verses three and nineteen is empasising different approaches to the same goal based on qualification so there is no contradiction.

Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

3.10 Pura, in the days of yore, in the beginning of creation; srstva, having created; prajah, the beings, the people of the three castes; saha-yajnah, together with the sacrifices; Prajapati, the creator of beings, uvaca, said; ‘Anena, by this sacrifice; prasavisyadhvam, you multiply.’ Prasava means origination, growth. ‘You accomplish that. Esah astu, let this sacrifice be; vah, your; ista-kama-dhuk, yielder of coveted objects of desire.’ That which yields (dhuk) coveted (ista) objects of desire (kama), particular results, is istakama-dhuk. How?

Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:

3.10 Saha-etc. The lord of creatures, the Supreme Soul, created creatures, just together with actions. It has also been declared by Him that the procreation i.e., lineage of creatures is through actions alone; these alone would give them what is desired viz., either the cycle of birth-and-death or emancipation – the cycle of birth-and-death is due to attachment and emancipation, due to the freedom from attachment. The sense-objects deserve to be enjoyed only by those for whom emancipation is the most important. This is declared :

Sanskrit Shloka Without Transliteration Marks:

saha-yajnah prajah srstva
purovaca prajapatih
anena prasavisyadhvam
esa vo ‘stv ista-kama-dhuk

Sanskrit to English Word for Word Meanings:

saha — along with; yajñāḥ — sacrifices; prajāḥ — generations; sṛṣṭvā — creating; purā — anciently; uvāca — said; prajā-patiḥ — the Lord of creatures; anena — by this; prasaviṣyadhvam — be more and more prosperous; eṣaḥ — this; vaḥ — your; astu — let it be; iṣṭa — of all desirable things; kāma-dhuk — bestower.