Page:Aryabhatiya of Aryabhata, English translation.djvu/34

4 which are arranged in five groups of five letters each. The avarga letters are those from y to h, which are not so arranged in groups. The phrase "beginning with ka" is necessary because the vowels also are divided into vargas or "groups."

Therefore the vowel a used in varga and avarga places with varga and avarga letters refers the varga letters k to m to the first varga place, the unit place, multiplies them by 1. The vowel a used with the avarga letters y to h refers them to the first avarga place, the place of ten's, multiplies them by 10. In like manner the vowel i refers the letters k to m to the second varga place, the place of hundred's, multiplies them by 100. It refers the avarga letters y to h to the second avarga place, the place of thousand's, multiplies them by 1,000. And so on with the other seven vowels up to the ninth varga and avarga places. From Aryabhata's usage it is clear that the vowels to be employed are a, i, u, r, I, e, ai, o, and au. No distinction is made between long and short vowels.

From Aryabhata's usage it is clear that the letters k to m have the values of 1-25. The letters y to h would have the values of 3-10, but since a short a is regarded as inherent in a consonant when no other vowel sign is attached and when the virama is not used, and since short a refers the avarga letters to the place of ten's, the signs ya, etc., really have the values of 30-100. The vowels themselves have no numerical values. They merely serve to refer the consonants (which do have numerical values) to certain places.