Verse 3.11.19

Sanskrit text, Unicode transliteration and English translation of verse 3.11.19:

सङ्ख्येयसङ्घसङ्ख्यानसङ्घः सङ्ख्येति कथ्यते ।
विंशत्यादिषु सान्यस्य द्रव्यसङ्घस्य भेदिका ॥ १९ ॥

saṅkhyeyasaṅghasaṅkhyānasaṅghaḥ saṅkhyeti kathyate |
viṃśatyādiṣu sānyasya dravyasaṅghasya bhedikā || 19 ||

19. In Viṃśati etc. the number is a collection of numbers measuring the things to be measured and it differentiates another collection of things.

Commentary

But numerals up to ten express number only, Viṃśati, on the other hand, expresses not only number but also what is numbered. The author now says something about such words.

[Read verse 19 above]

[They are also derived from the unities with the help of apekṣābuddhi. But they denote number as well as the thing numbered. We can say gavāṃ viṃśatiḥ where viṃśati = ‘twenty’ stands for number only or viṃśatir gāvaḥ where twenty stands for the cattle which are numbered. If, in the word viṃśati, the suffix is deemed to have been added in the sense of svārtha, there would be two disadvantages: (1) it would not be possible to form the compound viṃśatigavām, because viṃśati would have the meaning of the prakṛti, that is, pure number, two lens, (2) the word viṃśali cannot have the singular number because the meaning of the prakṛti is two things. The second defect is removed if the suffix is considered to have been added in the sense of the pariṇāmin but not the first defect. Secondly, we cannot have the expression viṃśako gosaṃghaḥ unless a special rule is made saying that ḍvun is added in svārtha, because viṃśati already stands for saṃgha. Thirdly, the sixth case affix as in gavāṃ viṃśatiḥ, would have to be taught because viṃśati really means so many cattle and not their collection. And yet the expression is quite correct. Thus derivation becomes difficult in the ease of the word viṃśatiḥ. Nor would it do to say that the word has no derivation. It has one. According to the Mahābhāṣya, the suffix in viṃśati is added in the sense of saṃgha or samudāya. This docs not make it necessary to say that ḍvun is added in the sense of svārtha because the suffix stip is taught in the sense of a collection of numbers, while ḍvun would mean a collection of cattle. Viṃśako gosaṃghaḥ would mean a collection of cattle of the size of a collection of two decades. There is really no difference here between a collection of cattle and a collection of decades. Words present them as though they were different. That is a characteristic of words. Thus in viṃśatiḥ, the suffix is added in the sense of collection and the word stands for number or dharma and it can be used in a double manner.]