बहु-गण-वतु-डति सङ्ख्या

This sutra defines the word sankhya, or numeral.

These are certain words, besides the ordinary numerals, having some peculiarity of declension. The words like बहु 'many,' and गण 'class', and those that have the affixes वत् and अति after them, belong to this class. The letters उ and ड of वतु and डति are इत्, or indicatory, the actual affixes being वत् and अति.

The word sankhya means
umerals;\ and this class contains, among others, the Sanskrit numerals. The words formed by adding वतु are generally compound pronouns, e.g. तावत् \so much,\ यावत् \as much,\ एतावत् \so much,\ similarly words formed by the affix डति, e.g. कति \how many,\ तति \so many,\ यति \as many.\

Thus बहु + कृत्वसुच् 5.4.17 = बहुकृत्वः \many times\ the affix कृत्वसुच् being added only to sankhya words in the sense of the repetition of the action. So also बहु + धा 5.3.42 = बहुधा \in many ways.\ Here also the affix धा is added by virtue of बहु being a sankhya. Similarly बहुकः 5.1.22 \purchased for a big sum,\ बहुशः 5.4.43 \manifold.\ So also गणकृत्वः, गणधा, गणकः, गणशः; so also तावत्कृत्वः, तावद्धा, तावच्छः, कतिकृत्वः; कतिधा, कतिकः, कतिशः.

When the words बहु and गण mean \abundance\ and \multitude\ they are not sankhya. It is only when they are expressive of numbers, that they get the designation of sankhya. The necessity of defining sankhya arose in order to exclude such words as, भूरि
umerous,\ &c., which though they express numbers, are not to be treated as
umerals,\ technically so called.

Vart:- The word अर्द्ध \half\ when standing as a first term in a compound number which takes an affix giving the sense of an ordinal, gets the designation of sankhya, for the purposes of the application of the rules of samasa and of the affix कन्. The ordinal affixes or purana pratyayas are like डट् 5.2.48, मट् 5.2.49, थक् 5.2.51, &c. Thus एकादशः \eleventh,\ पंचमः \fifth,\ चतुर्थः \fourth,\ &c. Similarly we have अर्द्धपंचशूर्पः \purchased for 41\/2 baskets\ (a dvigu). Here अर्द्ध + पंचमा (an ordinal) = अर्द्धपंचम्, a bahuvrihi compound meaning 41\/2, vis., that in which half is the fifth term. अर्द्धपंचमैः शूर्पैः क्रीतः = अर्द्धपंचमशूर्पः the taddhita affixes ठञ् and अञ् required by 5.1.19 and 5.1.26 being elided by 5.1.28.

Here, there is compounding (dvigu) by taking अर्द्धपंचमम् as a sankhya, and then applying sutra (II. I. 51). The samasa here is in the sense of taddhita, and this compounding is only possible by rules 2.1.50 and 2.1.51, when अर्द्धपंचमम् gets the appellation of sankhya. Having got this name, it forms dvigu compound in the sense of the taddhita affixes अञ् and ठञ् 5.1.26. The word शूर्प takes both these affixes in the sense of \being bought with.\ Thus शौर्पिकम् and शौर्पम् both mean \bought with a measure called surpa.\ In the above compound of अर्द्धपंचमशुर्पः the sense is that of the above-named taddhita; but the affixes have been elided by 5.1.28 after dvigu compounds. So also we have अर्द्धपंचमकः by applying the affix कन्. For these two purposes, namely samasa and the application of कन्, compounds of ardha, like ardha-panchama are treated as sankhya.,