LATER HINDU FORMS, WITH A PLACE VALUE
Before speaking of the perfected Hindu numerals with the zero and the place value, it is necessary to consider the third system mentioned on page 19,—the word and letter forms. The use of words with place value began at least as early as the 6th century of the Christian era. In many of the manuals of astronomy and mathematics, and often in other works in mentioning dates, numbers are represented by the names of certain objects or ideas. For example, zero is represented by "the void" (śūnya), or "heaven-space" (ambara ākāśa); one by "stick" (rupa), "moon" (indu śaśin), "earth" (bhū), "beginning" (ādi), "Brahma," or, in general, by anything markedly unique; two by "the twins" (yama), "hands" (kara), "eyes" (nayana), etc.; four by "oceans," five by "senses" (viṣaya) or "arrows" (the five arrows of Kāmadēva); six by "seasons" or "flavors"; seven by "mountain" (aga), and so on.[[130]] These names, accommodating themselves to the verse in which scientific works were written, had the additional advantage of not admitting, as did the figures, easy alteration, since any change would tend to disturb the meter.
As an example of this system, the date "Śaka Saṃvat, 867" (A.D. 945 or 946), is given by "giri-raṣa-vasu," meaning "the mountains" (seven), "the flavors" (six), and the gods "Vasu" of which there were eight. In reading the date these are read from right to left.[[131]] The period of invention of this system is uncertain. The first trace seems to be in the Śrautasūtra of Kātyāyana and Lāṭyāyana.[[132]] It was certainly known to Varāha-Mihira (d. 587),[[133]] for he used it in the Bṛhat-Saṃhitā.[[134]] It has also been asserted[[135]] that Āryabhaṭa (c. 500 A.D.) was familiar with this system, but there is nothing to prove the statement.[[136]] The earliest epigraphical examples of the system are found in the Bayang (Cambodia) inscriptions of 604 and 624 A.D.[[137]]
Mention should also be made, in this connection, of a curious system of alphabetic numerals that sprang up in southern India. In this we have the numerals represented by the letters as given in the following table:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| k | kh | g | gh | ṅ | c | ch | j | jh | ñ |
| ṭ | ṭh | ḍ | ḍh | ṇ | t | th | d | th | n |
| p | ph | b | bh | m | |||||
| y | r | l | v | ś | ṣ | s | h | l |
By this plan a numeral might be represented by any one of several letters, as shown in the preceding table, and thus it could the more easily be formed into a word for mnemonic purposes. For example, the word
| 2 | 3 | 1 | 5 | 6 | 5 | 1 |
| kha | gont | yan | me | ṣa | mā | pa |
has the value 1,565,132, reading from right to left.[[138]] This, the oldest specimen (1184 A.D.) known of this notation, is given in a commentary on the Rigveda, representing the number of days that had elapsed from the beginning of the Kaliyuga. Burnell[[139]] states that this system is even yet in use for remembering rules to calculate horoscopes, and for astronomical tables.