I was trying to learn hymns from this Rig Veda video. But I couldn't find the first few verses.
Where in the book is it?
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ghaṇānāṃ tvā ghaṇapatiṃ havāmahe kaviṃ kavīnāmupamaśravastamam |
jyeṣṭharājaṃ brahmaṇāṃ brahmaṇas pata ā naḥ ṣṛṇvannūtibhiḥ sīda sādanam ||
We call thee, Lord and Leader of the heavenly hosts, the wise among the wise, the famousest of all, the King supreme of prayers, O Brahmaṇaspati: hear us with help; sit down in place of sacrifice.
This was traditionally considered a mantra to Brihaspati the guru of the gods; see the Anukramani for Rig Veda Book 2 in my answer here. But because it contains the word "Ganapati", people often consider it to be a prayer to Ganesha.
ni ṣu sīda ghaṇapate ghaṇeṣu tvāmāhurvipratamaṃkavīnām |
na ṛte tvat kriyate kiṃ canāre mahāmarkaṃmaghavañcitramarca ||
Lord of the hosts, amid our bands be seated: they call thee greatest Sage among the sages. Nothing is done, even far away, without thee: great, wondrous, Maghavan, is the hymn I sing thee.
As you can see in the Anukramani for Book 10, this was traditionally considered a mantra to Indra, but again because it contains the word "Ganapati" people often consider it to be a prayer to Ganesha.
pra ṇo devī sarasvatī vājebhirvājinīvatī |
May the divine Sarasvatī, rich in her wealth, protect us well, Furthering all our thoughts with might
That is unambiguously a mantra to Saraswati, as you can see in the Anukramani for Rig Veda Book 6.
I can't quite make out the words of the fourth mantra, which goes from the 1:04 mark to the 1:22 mark of the video. (Can anyone else hear it?). But the fifth mantra is Rig Veda Book 1 Hymn 164 Verse 39; here is the Sanskrit and here is the English:
ṛco akṣare parame vyoman yasmin devā adhi viśve niṣeduḥ |
yastan na veda kiṃ ṛcā kariṣyati ya it tad vidusta ime samāsate ||
Upon what syllable of holy praise-song, as twere their highest heaven, the Gods repose them,— Who knows not this, what will he do with praise-song? But they who know it well sit here assembled.
As you can see in the Anukramani for Rig Veda Book 1, this mantra is dedicated to all the gods, but I suspect the reason they included this mantra in the chant was because of the meaning, which may be related to the Pranava.
And after the first five mantras they start going into Rig Veda Book 1 Hymn 1; here is the Sanskrit and here is the English. This hymn is dedicated to Agni the fire god, as you can see in the Anukramani for Rig Veda Book 1.