वृद्धिर्यस्याचामादिस्तद् वृद्धम्

That word, among the vowels of which the first is a वृद्धि , is called वृद्धम्।
This defines the word वृद्धम्. The sutra consists of five words :- वृद्धिः 'the vriddhi vowel;' यस्य 'whose,' अचाम् 'among the vowels,' आदिः 'is first;' तद् 'that; वृद्धम् 'is called vriddham.'

If a word consisting of many vowels, has a vriddhi vowel coming first in the order of vowels, that word is called vriddham. Thus the words माला, शाला &c., have the first vowel आ a vriddhi vowel, therefore, they are called vriddham.

The word vriddham has been defined in order to make applicable to these peculiar words certain taddhita affixes. Thus there is a rule 4.2.114 by which the affix छ् is added to vriddham. Thus माला + छ् = मालीयः ॥

Why do we say "the first?" Because a word like सभासंनयनः, which is not a vriddha word, will not admit of the affix छ्. Its corresponding derivative will be साभासंनयनः ॥

Vart:- A proper noun, though not coming under the above definition, may yet be regarded optionally as a vriddham. Thus देवदत्त + छ् = देवदत्तीया, or we may have दैवदत्ता.

Vart:- A compound ending in a Gotra word, is regarded for the purposes of the addition of this affix, as if it was not compounded. Thus रौढि is a Gotra word and also vriddham. Its compound घृतरौढि will be regarded as a vriddham too, for the addition of the affix. As घृतरौढि + छ् = घृतरौढीयाः 'the students of Ghritaraudhi.' So also ओदनपाणिनीयाः, वृद्धाम्भीयाः वृद्धकाश्यपीयाः &c.

Vart:- Exception must be made in the case of जिह्वाकात्य and हरितकात्य । They do not take छ्. Thus जैह्वाकाता and हारितकाताः.