Here is an example I took from another post here:
bhaskaraya vidmahe mahaddyutikaraya dhimahi |
tanno adityyah pracodayat
There are lots of variants of this formula. What is the context in which this formula is used and what does it mean?
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To answer your question lets breakdown all three
Vidmahe - root is vid - to know Dhimahi - root is Dhi - to illuminate Pracodayat - can be looked at as pra cod - to move towards or as rooted in prac to inquire.
I tend to think of the meaning in in reverse. Beginning with a prayer which is also a self inquiry - in your example tanno adityyah pracodayat - may we be moved towards Aditya - the self inquiry becomes who is this Aditya - this inquiry when deeply contemplated inspires you to move in the direction to discover the answer. Next in reverse we have Mahadyuti Dhimahi - so dhimahi typically is translated as to meditate, but we can look a little deeper and get a more colorful picture. Dhi is the light of consciousness that illuminates ones mindspace. So Dhimahi in this context is saying let my mindspace be illuninated with or by Mahadyuti - the greatly effulgent and glorious one. May my mind be completely absorbed in Mahadyuti - hence let me meditate on Mahadyuti. Next we have the opening bhaskaraya vidmahe - Vid means to know it is the root of words like vidya and veda. Vidmahe - means may I to come to knowing, to know, the object Bhaskara - The Shiner -
So then we can put it together properly. May I come to know Bhaskara - the One who Shines. May my mind be fully illuminated by the vision of Mahadyuti - the Greatly Glorious one. May we be moved by the inspiration of Aditya - the son of Aditi.
Dhimahi:- This word is derived from √dhi which means to worship or meditate. From V.S. Apte Dictionary;
Vidmahe:- It is derived from √vid which means to know or understand. Source
Prachodyat:- It is derived from √pracud which means to inspire.
Maharishi Dayananda translated the word dhimahi and prachodyat as mentioned above in Gayatri mantra.
The word to word translation of the mantra you gave in question is given here.