Several methods of wntl7'Q numerals '101

mentioned as Chandovioiti in the Apastamba-dhal'IDasUtra UOJ Sabara 11M C about 200 A D. and not later than 400 A D.) speaks of Pingala's work as on the same level with Panini"s sntra It is unnecessary to offer furliher proofs of the antiquity ofPingala's sntra.

There were several methods of writing numerals One was the place value notation, in whioh the same numeral has different values according to the place it occupies; for example, the fignre two may have the valne of only two or twenty or two hundred and so on accordlDg as it occupies the units place or tens place or hundreds place Another way IS that of employing words to denote complete numbers This was a veryreliab1e method when in astronomy huge figures had to be employed and works were not printed but only copied by hand. In ancient times, the writers of mss. might often omit zeros or other figures, but if words with a fixed meaning in relation to numbers were used, they would not be so easily dropped and as many W01'ks were metrical, the omission of a word, if any. might ha.ve been far more easily detected It is difficult to say when this system was introduced. By.t its beginnings are ancient For example, the word kf'/a. is used In the Taittiriya 1105 Brahmana in the sense of • four '. Vara.hamihira. (beginning of the 6th cenfiury A.D.I employs these word numerals but in the place value system (vide H of Dh. vol m p 897 n.17b3.) The following is a list of some of the V6Ty USIlaJ. numbers with the corresponding words employed to indicate them It should be noted that the hat is not exhaus-tive. Any number of Sl"llonymsllD6 may be employed to indicate the same number. Vide the lists in Alberuni (Sachau, vol. I. pp. 1'14:-179) and Buhler's' IndIan Paleography' Cl A. vol 33; appendix pp. 83-86 )

1103. I ...miM I 3tl1I 1if .. n 4 8 10-11

1104. o;rfi t,'Zlfu,=;l ... 31QliuMUTiiiii<d .. G

'Ill! iNl a!bi\ulliillf Boe4 ';01 e=woi'tl... JIiIr.la '" I ' !II'n:'s DD 'l.{«H.iiel<fi 1 1. S. P 54.

1105 1'ril m(1 'lIT I 5 11. 1 1106 4:e4Iii'iiiil

(liS ID BhaD Da]1 Collection oC the Bomha} Asiatic Society) ror e'Cample, It may be 1l0ted that the lfl'l1es tv. enly-five syuonyms for iD oue place, beSides aud meul10ncd e1sea.bere as d" ine bClngs. ThIS work (In I 17-25) gives a. hst of the important word numerals as fullows H '!('q' .MUI .. " .. '

(Contir.lle4 on net /llZgc J

702

Zaro-SiiDl"a, kha, ambara ( sk;y). gagana, abhra Wm, binda, piirna. U07 •

One-eka, bhiimi ( earth). Indu ( the moon). rapa, Idf, ViSn11.

Two-dvi, aksi or looana (eye >, paksa. ASvin. dasra, dos or dosan ( arm), bhUJa, l"aIDa or l"amala (nvlllS)

'.l'hree-tri, krama (from three steps of Visnu in ago 1 22. 18 L 155. 5 ). grama ( 1D music "Rima, pura ( oitles burnt by RUdra ). lob ( earth, heaven and hell J. guna ( sattva, raJas, tamas ), agni (garhapatl"a. illavanIya and daks1nigni ).

Four-Catur, abdhi (ooean J. krta, yuga, veda, aruti, varna ( brilunana eta. )

Five-pancan, fsu or sara (arrows of Madana >, viyn (priDa, apina &0 ), bhiita (prlnu;, waters, teJas, air, iiMiia), aksa ( sense organ ), indriya, Pindava or Pindu-suta. .

Six-Sat, rasa (sweet, ao1d, salt &0 ), anga (tbe six auxiliary soiences of tbe Veda J. rlu (ssasons), tarka (lOgICal oategories from drall1Ja to sama"aua). darsana (SlX

of phIlosophy) Seven-Saptan, rsi or muni ( the seveD saps), svara (niSida,

rsabha &e. in music J. asv8 (seven horses of lihe Bun, who IS called • saptasva ' in ago V 45 9), girl, parvata ( Mahendra, Ma.la.ya, Sabya &0 ). dhita (elements of the body, viz skin. blood &0 ).

Elght-astan, vasu, sarpa (vide note 321 for eight nlgas). mangala, matangala (elephants of eIght quarte:rs ), siddhi ( anima, laghiml &0 in yoga.).

Numerals znd,cated by words 'loa Nine-navan, sankhya: (from 1 to 9), Nanda (nine Nands. kings),

l'andbra m: ohidra, nidlu ( treaS1ll'6, mahapadma, sankha, maks.ra &0 ), anka ( numel'als one to nine ), go m: graha or nabhascara (planets )

Ten-daaan, paiikti, 11117.. Asii. or diSii ( direotions inclnding ilrdh"a and adhara ). avat!ira, Riivana-siras.

Eleven-Ekidasan, Maheilvara, Rlldra. Twelve-dvii:dasan, aditya, arks. siirya, misa Thirteen-trayodasan, ViSve ( visve-devii.h ). Fourteen-oaturdasan, Manu, Indra, bhuvana (worlds, bhiih &0.

seven, and seven piitalas ). Fifteen-paiicadasan, tithi Sixtesn-sodasan, kala (digIts of the Moon" nrpa or rajan UD8

( kings ), asti Seventeen saptadasan, atyasti. EIghteen-astidasan, dhrti Nineteen-ekonavimsati, atidhrti Twenty--vimsati. krti. nakha (naIls), anguli C fingers of the

hands and feet together ). Twentyone-ekavimsati. prakrti. mtirChani ( in mnsic) Twantytwo-dvivimsati, jati, ikrti Twenfiyfonr-oaturvimsati, Jina or siddha (24 Jain tIrthankaras). Twentyfive--paiicavimsati. taltba (i5 Sii.nkhya principles. vide

note 1092) Twenliyseven-aaptavimsati, bha, naksatra Thirtytwo-dvatrimsat, dasana. or dvija ( both mean 'teeth'). Thirtytbree-trayastrimsat. sura ( gods ). Fortynine-akonapaiicisat, tina ( notes in mnsio )

The above method of employing particular significant words to denote certain numbers even in decimal place value system is largely employed by Varahamihira in his Paiicesiddhiintiki (e. g L 8 in note lOO.l above, v.m. 1)

1107 a. 'Qi(fifitnlial'ilsi5irilitsiW .... '5iilOQmaa.1sfliii .. ,,(BsidQ;" qt VI 1 59.

1108. There IS & 'oi\ .. 4I<i3I ... 'lQ' section in chap 55-71 (16 aDCll!nt 11DgS Damed Saholra, Paarava &.c.). Asb IS & VedlC metre, each of its four pidas haVIng 161etlers as ID. Rg II 22 1; is another Ved\C metre With 68 letters ID {oar pidas. Dhrl1, Abdbrl1 Krtl, Prairb, aad Akrti have respectively 72. 76, 80 84, 88 letters In ;"11 pidas, Tbe Rk-prituiUy& (16 83-90) S'a) s onmt'ElQi!; q\i'. , I 1[f.f fimmI I I 'Om. I qcil..-nif.

'6h"StWfiI ... ElQa n ' .. cd by Dev& Sbastd, Allahabad (1931 )

704 HZ8tor]J of DharmaliiBlra l Sec. n, Oh, XIX

and In Brhat-samhiti 8. 20 and by all later astronomIOal writers U09 The partioular matter to be noted IS that the first word in a. grOUP (denotIng a number) is to be assigned to the units next to its left in the tans place, so that a word lIke saptisVl-veda.-sankhyam' becomes 4a7 ( by the rule ankinim va.mato gatfh ' )

Another method for expressing numbers IS elaborated by Aryabhat& in his 11111 ( verse 3) where the letters from Tt (kI. also) to m have the values of 1 to 25, whIle yu, ,a,la, va, sa. Ba, Ba and ha stand for 30, 40, 50, 60, 70, 80, 90 and 100 and so on towards mora complicated matters

The fourth anga in a panolnga is called Yoga. There lS no direot astronomioal phenomena correspondlng to it It is caloulated from. the sum. of the longltudes of the Sun and the Moon (or it is the time during which the sun and the moon together accomplish 13 degrees and 20 minutes at space) When thIS amounts to degrees 13 20 the first Yoga called Vlskambha ends; when it amounts to 26. 40 the 2nd Yoga. Prltl ends and so on. The yogas are 27 ( tha.t thns make 360 degreae) as stated in the Ratnamilii.lV. 1-3 and are as follows -

Name Deity 1. Viskambha-Yama 2. Prlti - VIsnu 3 Ayusmat-Candra. 4 Saubhigya-Biahml 5 Sobhana - Brhaspati 6 Atiganda-Oancira 7 Sukarman-8. Dhrtf-Apah 9 Siila-Sarpa

10 Ganda- Agni 11 Vrddhi - Siiry-a 12 Dhruva-Prthvt 13 Vyilghita-PavanB 14. Harsana-Rudra

15 16. 17. 18. 19

VSoJEa-Varuua Slddhi-Ganeila VyatIpitB-SIV&. Variyas- Kubara Parigha-Vlsvaltarma.u

20 Siva-MItra 21 Siddha-Kirtlkeya 22. Sidhya - BivitrI 23 Subha-Kama1l: 24 Su.kla-Gaul'I 25. Brahman - ABVlnaU 26 Aludra-Pltrs 27 Valdhrti - Aditl

b 1109. How neatly huge numbers can be IndIcated by words may ,; dlustrated by the Rt I 28 -mt'r-iF.tlbdiii\4,. ... ,.i}:q*il' -a- Cl ....... mu " These come to 1972947179 day • ... iIII ... ' .. ."dl"1I1 .. ., q'" d by io Tbe Dakgillki vex88 3 has beeD ddfexeDtly Interprcte •

11 • ho'-- VIde Fleet 111 JRAS In 1911 pp 109-12a for Xrrabbata • different se ' .... g

system al1d pp 115-1l1S lor explanatlol1 of the verae