Page:Aryabhatiya of Aryabhata, English translation.djvu/37

Rh add two zero's to the numerical value of the consonant. This, of course, will work from the vowel i on, but the vowel a does not add two zero's. It adds no zero's or one zero depending on whether it is used with varga or avarga letters. The fact that khadvinavake is amplified by varge 'varge is an added difficulty to the translation "zero." It seems to me, therefore, preferable to take the word kha in the sense of "space" or better "place." Later the word kha is one of the commonest words for "zero," but it is still disputed whether a symbol for zero was actually in use in Aryabhata's time. It is possible that computation may have been made on a board ruled into columns. Only nine symbols may have been in use and a blank column may have served to represent zero.

There is no evidence to indicate the way in which the actual calculations were made, but it seems certain to me that Aryabhata could write a number in signs which had no absolutely fixed values in themselves but which had value depending on the places occupied by them (mounting by powers of 10). Compare II, 2, where in giving the names of classes of numbers he uses the expression sthanat sthanam dasagunam syat, "from place to place each is ten times the preceding."

There is nothing to prove that the actual calculation was made by means of these letters. It is probable that Aryabhata was not inventing a numerical notation to be used in calculation but was devising a system by means of which he might express large,