terpretation is acceptable. However, I know no other passage which, would warrant such a translation of antyavarge.
Sarada Kanta Ganguly translates, "'[Those] nine [vowels] [should be used] in higher places in a similar manner." It is possible for va to have the sense of "beliebig," "fakultativ," and for nava to be separated from antyavarge, but the regular meaning of antya is "the last." It has the sense of "the following" only at the end of a compound, and the dictionary gives only one example of that usage. If navantyavarge is to be taken as a compound, the translation "in the group following the nine" is all right. But Ganguly's translation of antyavarge can be maintained only if he produces evidence to prove that antya at the beginning of a compound can mean "the following."
If nava is to be separated from antyavarge it is possible to take it with what precedes and to translate, "The vowels (are to be used) in two nine's of places, nine in varga places and nine in avarga places," but antyavarge va remains enigmatical.
The translation must remain uncertain until further evidence bearing on the meaning of antya can be produced. Whatever the meaning may be, the passage is of no consequence for the numbers actually dealt with by Aryabhata in this treatise. The largest number used by Aryabhata himself (1, 1) runs to only ten places.
Rodet, Barth, and some others would translate "in the two nine's of zero's," instead of "in the two nine's of places." That is to say, each vowel would serve to
