Pāṇini sūtras

The affixes añ and ṭhañ come in the remaining senses after the word ‘ardha’, preceded by a word denoting direction, when a particular portion of a village or an inhabited country is meant.

1. grāma+janapada+eka+deśātग्राम+जनपद+एक+देशात्

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   gग्	grāmaग्राम	grāmaग्राम	village	grāmग्राम् + plus aअ
   jज्	janapadaजनपद	janapadaजनपद	country	janapadजनपद् + plus aअ
   eए	ekaएक	ekaएक	one	ekaएक
   dद्	deśaदेश	deśātदेशात्	part	deśदेश् + plus ātआत्

2. añ+ṭhañauअञ्+ठञौ

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   aअ	añअञ्	añअञ्	añअञ्	añअञ्
   ṭट्	ṭhañठञ्	ṭhañauठञौ	ṭhañठञ्	ṭhañठञ् + plus auऔ

Anuvṛtti

1. ardhātअर्धात् 4·3·4

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   aअ	ardhaअर्ध	ardhātअर्धात्	ardha [word]	ardhअर्ध् + plus ātआत्

2. diś+pūrva+padātदिश्+पूर्व+पदात् 4·3·6

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   dद्	diśदिश्	diśदिश्	direction	diśदिश्
   pप्	pūrvaपूर्व	pūrvaपूर्व	antecedent	pūrvaपूर्व
   pप्	padaपद	padātपदात्	word	padपद् + plus ātआत्